Basic Properties
Free (non-interacting) fermionic fields obey canonical anticommutation relations, i.e., involve the anticommutators {a,b} = ab + ba rather than the commutators = ab − ba of bosonic or standard quantum mechanics. Those relations also hold for interacting fermionic fields in the interaction picture, where the fields evolve in time as if free and the effects of the interaction are encoded in the evolution of the states.
It is these anticommutation relations that imply Fermi–Dirac statistics for the field quanta. They also result in the Pauli exclusion principle: two fermionic particles cannot occupy the same state at the same time.
Read more about this topic: Fermionic Field
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